Notes on f(R) Theories of Gravity

TL;DR

This review explores f(R) gravity theories, their boundary terms, equivalence to scalar-tensor theories, and their application to cosmological models, providing foundational insights into modified gravity approaches.

Contribution

It offers a comprehensive overview of f(R) theories, including boundary terms, conformal transformations, and their cosmological implications, which is a valuable synthesis for researchers in modified gravity.

Findings

f(R) theories can be transformed into scalar-tensor models

Boundary terms in f(R) gravity are crucial for well-posed variational principles

f(R) cosmological models can replicate standard cosmological behaviors

Abstract

In this review paper we present some basic notions about f(R) theories of gravity and some simple cosmological models derived from it. We first make an introduction to General Relativity (GR), followed by the discussion of Gibbons-York-Hawking boundary term in GR. We also discuss boundary terms in f(R) theories and the application of conformal transformations in order to show that f(R) theories can be made equivalent to GR minimally coupled with a scalar filed. In the final sections of the paper a brief review of classical Friedman and Lemaitre cosmological models is made, followed by the discussion of cosmological models derived from f(R)gravity.